Sic is (1) a Latin-derived word used to indicate that quoted text is reproduced as it originally appeared, and (2) a verb meaning to set upon or to incite to hostile action. For example, you might sic your dog on a snake. Sick, which is never a verb (except, rarely, in the colloquial phrasal verb sick up), is a misspelling when used in this sense.
Sic is inflected as sicced, siccing, and sics. Your spell check might say these forms are wrong, but spell check is behind the times in this case.
Now in Morocco, the Jays sicced monkeys on the girls as they toured a Marrakech market. [New York Magazine]
Police say a man who tried to sic his pit bull on a neighbour ended up being attacked by his own animal. [Toronto Sun]
Yesterday he learned that the Quebec government is siccing its anti-corruption unit on city hall. [Montreal Gazette]